Do you think it would be hard being 28 going into med school as a veteran?
Not at all. Average age of a med student is 24, so you're not that far off. I matriculated at 30. In fact, you'll probably be in better shape than most. With your GI money, you should be debt free after undergrad.
Military medicine isn't an option.
Why not military medicine? I assume you don't want to be career military? Granted this is a decision you will be making 10 years from now and your thoughts are bound to change and evolve, but don't discount it now. There are three great options for military medicine, but I only have experience with one.
USUHS - Uniformed Services University of Health Science - It's the military's medical school outside of DC. It's a great school with probably the best/advanced/coolest simulation center in the country. Through school you'll be rated as O-1 with full active duty pay + COLA (if you were enlisted for 5 years, that will be added into your active duty pay scale). When you graduate you'll be promoted to O-3 and then O-4 after residency. You'll owe back 7 years of service going this route. With your 5 years after HS, 4 year residency (taking the average here), and 7 year commitment, you'll only be 4 years away from retirement (time at USUHS doesn't count towards retirement, but does towards pay grade). That means by 48, able to work as a civilian doc for the next 15-20 years, with zero student debt, and be collecting military retirement pay at the same time. Not to mention, if you're Marines, that technically puts you under the Navy as a Medical Officer. Besides line officers, you're the highest ranking officers if you're in country or with the fleet.
I was accepted to USUHS and personally would have matriculated, but my wife, despite the financial benefit, was opposed to the time away from family the service would require.
So for right now, if you want to enter the Corps, I would say do it. It def. isn't a negative and will only help you focus your future career aspirations. Semper Fi.